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Analysis of the 3/2 Power Law of Self-Thinning

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The 3/2 power law states that the relative rate of self-thinning with respect to biomass growth per unit area is a universal constant equal to two. The law could be true in two cases: (1) when all factors of stand dynamics unaccounted for by the law (in particular, change in plant form and change in crown closure) are nonexistent; and (2) when the effects of the unaccounted factors on the rate of self-thinning cancel each other. As the presented reasons and evidence show, the major neglected factors indeed oppositely affect the rate of self-thinning. In general, however, these factors rarely balance each other, and the rate predictably changes with age, species, site quality, and other factors. The limiting line of self-thinning does not have any constant slope (on the log-log scale); generally, this line is a curve. A realistic model of self-thinning should be more inclusive than the law and particularly reflect the change in crown closure, or gap dynamics. An analysis of the law suggests the use of tree size as a predictor of their number; the utilization of the fact that diameter is better correlated with crown width and tree number than tree mass; and the development of a more adequate form of expressing allometric relationships than the elementary power function. For. Sci. 33(2):517-537.
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Keywords: Allometric regression; Reineke's equation; crown closure; gap dynamics; stand dynamics; tree morphology

Document Type: Journal Article

Affiliations: Professor of Forestry, Department of Forest Resources, University of Arkansas at Monticello, and Arkansas Agricultural Experiment Station, Monticello, AR 71655

Publication date: 1987-06-01

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  • Forest Science is a peer-reviewed journal publishing fundamental and applied research that explores all aspects of natural and social sciences as they apply to the function and management of the forested ecosystems of the world. Topics include silviculture, forest management, biometrics, economics, entomology & pathology, fire & fuels management, forest ecology, genetics & tree improvement, geospatial technologies, harvesting & utilization, landscape ecology, operations research, forest policy, physiology, recreation, social sciences, soils & hydrology, and wildlife management.
    Forest Science is published bimonthly in February, April, June, August, October, and December.

    2016 Impact Factor: 1.782 (Rank 17/64 in forestry)

    Average time from submission to first decision: 62.5 days*
    June 1, 2016 to Feb. 28, 2017

    Also published by SAF:
    Journal of Forestry
    Other SAF Publications
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